TREATMENT WETLANDS - CHAPTER 6 doc

Most of the existing treatment wetland literature considers the probability distri-butions of the raw data for concentration time series.. The phosphorus concentration produced in treatm

This chapter examines the available means of collecting and

analyzing the large amount of performance data that now

exists for treatment wetlands Wetlands are “open” systems

heavily influenced by environmental factors This makes

them more complex than other types of biological treatment

reactors (activated sludge, trickling filters) described in the

environmental engineering literature Nevertheless, attempts

have been made to adapt models from these other

technolo-gies to treatment wetlands (Burgoon et al., 1999; McBride

and Tanner, 2000; Langergraber, 2001; Rousseau et al.,

2005b; Wu and Huang, 2006) Wetlands are dominated by

biomass storage compartments that are very large relative

to pollutant mass in the water column (again, different than

other biological reactors) These biomass storage

compart-ments are affected by seasonal cycles that are different than

temperature cycles

Treatment performance is represented by two

compo-nents: the central treatment tendency for a wetland (or group

of wetlands) and the anticipated variability away from that

central tendency Central tendencies are driven by flows

and concentrations, in concert with environmental factors

Random events within the wetland will produce stochastic

variations in effluent performance Both must be assessed to

describe treatment performance in constructed wetlands

Different types of wetlands (e.g., wetland configuration,

vegetative community) function differently Therefore, a set

of “universal” parameters for describing treatment

perfor-mance in wetlands is not to be expected

6.1 VARIABILITY IN TREATMENT WETLANDS

Two types of variability are of interest for understanding

and design of treatment wetlands First, it is necessary to

understand the scatter of performances for an individual

wetland, around either the central tendency of data or

the model characterization of that central tendency This

is the intrasystem, or internal variability, and it is needed

to understand the excursions that may be expected, and to

design to meet permit requirements that involve allowable

maximums Internal variability includes seasonal,

stochas-tic, and year-to-year changes Wetland performance can also

change from year to year due to changes in vegetative

com-munities, hydraulic or organic loadings, or weather

condi-tions Second, it is useful to understand how comparable

wetlands vary, which is the intersystem variability Causes

of this variation will include factors such as vegetation

spe-cies, system geometry, and climatic conditions Both types

of variability are best explored by graphical methods

Data frequency influences the degree of scatter in data ability decreases daily–weekly–monthly–annual, but the central tendency is the same For example, the coefficients of variation for total phosphorus over four years at Brighton, Ontario, were weekly  89%, monthly  83%, and annual  19%

Vari-Many factors contribute to random variability in the let concentrations from a single treatment wetland This vari-ability is typically not small, with coefficients of variation of 20%–60% being common Deterministic models reproduce the central tendency of performance, but not the random variability Whether there is microbial or vegetative control, seasonal patterns of wetland variables are the rule, accompa-nied by a random variable term (Kadlec, 1999a)

A choice may be made to either deal with “raw” data or detrend a concentration time series using either a mecha-nistic model or a cyclic annual trend Most of the existing treatment wetland literature considers the probability distri-butions of the raw data for concentration time series The typical method is to present the cumulative probability distri-butions for concentrations entering and leaving the wetland (see, e.g., Kadlec and Knight, 1996; U.S EPA, 1999) Typical probability distributions are shown for weekly average for data Columbia, Missouri (Figure 6.1) The median inlet BOD

 26 mg/L in 1995, while the median outlet BOD  9 mg/L However, inlet concentrations ranged from 8 to 60 mg/L, and outlets from 4 to 24 mg/L At the weekly time scale, the maximum BOD exiting the wetland was 2.7 times the median The data in this BOD example are not detrended.Seasonal changes in treatment performance can often be represented by cosine trends (Kadlec, 1999a)

Stochastic variability will report as a “cloud” around the seasonal trend line:

average (trend)avg

C  ooutlet concentration, mg/Lrandom portion

E of the outlet concentration, mg/Ltime o

t ff the year, Julian daytime of the yea

max

concentration, Jullian day

The deterministic portion of this representation may in turn

be modeled by the k-rate technique with appropriate rate

constants and background concentrations, both of which

may respond to temperature and season, as will further be

discussed

The existence of the error term (E) means that sampling

must either be at high frequency or cover many annual cycles

before meaningful trend averages can be determined Data

from several years may be “folded” to create an annualized

grouping, distributed across the year according to Julian day

This use of many annual cycles has the advantage of

includ-ing year-to-year variations in climate, flow, and ecosystem

condition

The stochastic portion (E) will have a probability

dis-tribution, which will be different depending upon sampling

frequency and sample averaging period The ammonia

con-centration data for Columbia, Missouri, serve to illustrate

that stochastic variability may be considered separately from

annual trends At that site and most other treatment wetlands,

there is a strong annual cycle in ammonia, occasioned by the

slow-down in treatment during the winter months, as well

as by trends in the ammonia levels leaving pretreatment

(Figure 6.2) For that FWS system, Equation 6.1 was

cali-brated to the data from 1994 to 1995 as follows:

The variability in the inlet and outlet concentrations may then

be expressed as fractional departures from the trend values,

which is the random variable denoted by E/C from Equation

6.1 The cumulative probability distributions for both inlet

and outlet time series are similar (Figure 6.3)

I NTERSYSTEM V ARIABILITY

Apart from the concept of how one wetland may vary in its

performance, there is the issue of how the parameters of the

deterministic portion of the wetland performance model change from system to system Typically, the difference in treatment performance between wetland systems is much greater than the difference in performance within a particu-lar wetland system There are several ways to express this variability, including:

Side-by-side comparisons of wetlands with ent attributes, such as type, or presence, or absence

differ-of vegetationDistributions of model parameter values, such as

k-values, across a large number of comparable

wetlandsGraphical performance comparisons for sets of wetlands, based upon some period of performance such as annual or entire period of data recordThe key to assigning differences to “variability” is the process

of accounting for the principal factors affecting performance

FIGURE 6.1 Distribution of BOD concentrations measured at the

Columbia, Missouri, FWS wetlands in 1995 (Unpublished data

from city of Columbia.)

0 5 10 15 20 25

Julian Day

Outlet Trend

FIGURE 6.2 Ammonia nitrogen concentrations leaving the

Columbia, Missouri, FWS wetlands in 1995, together with the annual trend Data were acquired daily on weekdays (Unpublished data from city of Columbia.)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Fractional Error

Inlet Outlet

FIGURE 6.3 Distribution of ammonia concentration fractional

departures from annual trends measured at the Columbia, Missouri, FWS wetlands in 1995 Derived from the data in Figure 6.2.

separately and in advance of comparison For example, the

methods for describing effects of detention time or hydraulic

loading, inlet concentration, temperature, and season will be

discussed in the following text It is clear that it is not

use-ful to compare the summer behavior of one wetland to the

winter behavior of another, because we have already

identi-fied the potential for seasonal and temperature differences

A choice that minimizes seasonal effects is the annual

aver-aging period, which retains climatological effects, such as

mean annual temperature and rainfall

Two wetlands of the same size and type should be expected

to perform similarly if they receive identical water flows

and concentrations This has generally been observed to be

the case in the few side-by-side studies that have involved

such replication (see, e.g., Moore et al., 1994; CH2M Hill and

Payne Engineering, 1997; CH2M Hill, 1998; Mitsch et al.,

2004) Typical effluent concentration patterns follow similar

time series, with occasional differences of unknown causes

(Figure 6.4) Because of the expense of building and

moni-toring replicated wetlands, most of the comparative studies

of treatment wetlands have not involved replication; this is

apparently a justifiable step

S IDE - BY -S IDE S TUDIES

There have been numerous side-by-side studies conducted

to elucidate possible effects of vegetation type, media size,

aspect ratio, and other factors In general, such studies have

not involved replication, as noted in the previous text In

these studies, the incoming water chemistry and often the

inlet flow rates are the same Climatological effects, such

as rainfall and air temperature, are identical for the

com-parison systems The results of side-by-side testing

deter-mine the effect of the tested variable, but only for the

specific circumstances of test wetland systems For instance,

Wolverton et al (1983) bench-tested Phragmites and rushes (Schoenoplectus (Scirpus) spp.) in HSSF wetland

bul-microcosms and determined a significantly better

perfor-mance for Phragmites On the other hand, Gersberg et al (1986) tested Phragmites and bulrushes (Schoenoplectus (Scirpus) spp.) in outdoor pilot HSSF wetland environments

at Santee, California, and determined a significantly better

performance for Schoenoplectus However, when the same

plants were tested in a full-scale HSSF facility at Minoa,

New York (Liebowitz et al., 2000), essentially no difference

was found for COD and other parameters (Figure 6.5) These analyses emphasize the need for great care in detailing the circumstances of side-by-side studies Further extrapola-tions to other situations may be very misleading, however similar the circumstances may be

Combining performance data from different wetland systems

to create an aggregated data set results in data clouds that have considerably more variability than the individual wet-land data sets they were created from These aggregated data sets are useful for exploring the bounds of treatment perfor-mance in a particular application, but may not accurately pre-dict the performance of an individual treatment wetland.Aggregated data sets can be used to define the central tendency in treatment performance for a given type of wet-land reactor and application (e.g., BOD removal in HSSF wetlands) However, use of the central tendency to create a

“rule of thumb” is only one piece of the description of ment performance Because of the loss of specificity and high variance in these aggregated data sets, statistics such as confidence intervals and effluent multipliers have to be devel-oped to assess short-term variances that may be important for risk assessment

treat-0 10 20 30 40 50 60 70 80 90

Time (months)

Inlet South Test Cell #3 South Test Cell #8

FIGURE 6.4 Performance of two FWS wetland replicates for phosphorus reduction at low concentrations These behave similarly over

most of the period of record The reason for departure during the last three months of the record is not known (Unpublished data from South Florida Water Management District.)

6.2 GRAPHICAL REPRESENTATIONS OF

TREATMENT PERFORMANCE

There exist a large number of data sets for some of the more

common pollutants, such as TSS, BOD, phosphorus, and

nitrogen species Several types of graphs may be used to

compare performances across systems, and these have been

used in prior treatment wetland literature:

1 Output concentration versus input concentration

2 Output concentration versus input areal loading

3 Output loading versus input loading

4 Load removed versus input areal loading

5 Rate constant versus input areal loading

The first two of these are useful representations, but the last

three very often lead to spurious relationships that serve no

useful purpose Many important variables are lost in these

plots, because of their restrictive 2-D nature

The input–output concentration graph essentially extends the

idea of percent removal to a group of wetlands That is useful

in obtaining first estimates of the potential of a class of

treat-ment wetlands to reduce a particular contaminant But, that

plot is of no value in sizing the wetland, because it does not

contain any information on the detention time or hydraulic

loading

The phosphorus concentration produced in treatment

wetlands depends upon three primary variables (area, water

flow, and inlet concentration), as well as numerous

second-ary variables (vegetation type, internal hydraulics, depth,

event patterns, and others) It is presumed that the area effect

may be combined with flow as the hydraulic loading rate

(q HLR) since two side-by-side wetlands with double the

flow should produce the same result as one wetland

There-fore, two primary variables are often considered: HLR

and inlet concentration (Ci) Older kinetic removal models

(e.g., the k-C* model) and performance regressions are based

upon these two variables (Kadlec and Knight, 1996).Later in this chapter, it will be shown that wetland outlet concentrations are often well represented by:

o i

o i

C C

 llic loading rate, m/dHere this model is used to explore the expected correspond-ing appearance of intersystem performance graphs

An equivalent approach is to rearrange the primary ables, without loss of generality, by using inlet loading rate (LRI  q·Ci) and concentration (Ci) Thus, it is expected that

vari-the effluent concentration produced (Co) will depend upon

LRI and Ci A graphical display has often been adopted in the literature (Kadlec and Knight, 1996; U.S EPA, 2000a)

In the broad context, multiple data sets are represented by

trends that show decreasing Co with decreasing LRI, with a different trend line associated with each inlet concentration (Figure 6.6) For low inlet concentration or for higher hydraulic loadings, the log–log slope of the data cloud is approximately 0.33 (Figure 6.6), but the resultant outlet concentration range moves upward to higher values The right-hand asymptote of each data group, at very high pollutant loading, is an outlet concentration equal to the inlet concentration—or in other words, no removal The left-hand asymptote, reached only for

low inlet concentrations, is the background concentration, C*

The fact that there exist data clusters for each inlet range cates that there are at least two major factors influencing outlet concentration: inlet concentration and inlet loading

indi-0 100 200 300 400

FIGURE 6.5 Performance of side-by-side wetlands at Minoa, New York, vegetated with Phragmites spp and Scirpus (Schoenoplectus) spp

(Data from Theis and Young (2000) Subsurface flow wetland for wastewater treatment at Minoa Final Report to the New York State Energy

Research and Development Authority, Albany, New York.)

If the entire set of points in Figure 6.6 is considered,

ignoring the effect of inlet concentration, the general trend

line has a log–log slope of about 1.0 However, such a

sin-gle variable plot is nonunique, because of the effect of inlet

concentration, and may be misleading For instance, use of

a small intersystem data set might result in use of left data

points for high Ci, as well as right data points for low Ci, thus

exaggerating the slope Consequently, the Co– LRI graph

advocated in some literature (U.S EPA, 2000a) is

inade-quate The P-k-C* model typically spans the entire cloud of

intersystem results when exercised for various choices of Ci,

k, and C* (Kadlec, 1999c) It is expected that real data would

display behavior like that in Figure 6.6, and that expectation

is found to be realized in later chapters concerning individual

contaminants

The outlet concentration load graph is a useful addition

to the design sizing toolkit for treatment wetlands However,

it cannot be used in isolation as a design sizing basis, because

it does not separate the individual effects of inlet

concentra-tion and hydraulic loading Inspecconcentra-tion of Figure 6.6 shows

that the inlet loading is not a unique design variable, and that

the hydraulic loading and inlet concentration that define it

are not interchangeable Part II of this book discusses the use

of a concentration-loading graph as an important component

of the design process

The principal tool or examination of intersystem

variabil-ity in this book will be the outlet concentration versus inlet

loading graph The period of data averaging involved for

comparison purposes should be long enough to encompass

as much as possible of the intrasystem or internal

variabil-ity, so as to focus on system differences The operations of

the systems being compared should be past start-up, so that sustainable performance can be analyzed A subtle paradox occurs due to the fact that periods of record will not typi-cally be equivalent among comparison wetlands, except in

side-by-side studies Suppose Wetland A has two years and Wetland B has ten years, respectively, of data past start-up Neither Wetland A nor Wetland B will necessarily operate

or perform in the same way from year to year, so the choice

of annual averaging will produce two distinct data points for

Wetland A and ten for Wetland B There will be interannual

variability represented for each, which will, to some extent,

obfuscate the comparison between Wetlands A and B Thus

there are two logical choices: the use of interannual, system information, involving one point for each year for each wetland; and the use of period of record (POR), inter-system data, involving one point for each wetland

inter-These concepts are illustrated in Figure 6.7 for rus reduction for two similar wetlands treating facultative lagoon effluents Brighton provides some phosphorus removal via alum pretreatment, with a long-term mean influent of 0.45 mg/L In contrast, the inlet to the Estevan (Saskatchewan) wetlands was 2.26 mg/L Removal was 24% at Estevan, at an average hydraulic loading of 2.6 cm/d over a nine-year period

phospho-of record past start-up Removal was 40% at Brighton, at an average hydraulic loading of 5.1 cm/d over a 4.25-year period

of record (POR) past start-up Data are shown as monthly, annual, and period of record averages of weekly measure-ments The monthly data scatter is in part due to seasonal differences, which spanned May through November for Este-van, and all 12 months for Brighton This seasonal effect is removed by annual averaging, which causes only interannual and intersystem effects to remain Finally, interannual effects are removed by constructing the period of record averages, involving four years for Brighton and nine years for Estevan

FIGURE 6.6 Hypothetical concentration load response for the P-k-C* model, with P  3, k  6 m/yr, and C*  0.02 mg/L The lines are for

different values of influent concentration, as indicated in the legend On each line, the hydraulic loadings are from left to right: 0.25, 0.50, 1.0, 2.0, 5.0, 15.0, and 30.0 cm/d.

The reasons for the differences between these two systems

cannot be determined from the graphical representation

How-ever, as shall be seen in Chapter 10, much of the difference is

attributable to the nonuniqueness of the phosphorus-loading

variable, meaning that the difference in inlet concentrations

places the two systems in different groupings

It is also possible to look further via the P-k-C* model

There are no tracer tests of either wetland, so it will be

pre-sumed that N  P  4 It is known that C* is quite low for

phosphorus, and it will be presumed that C* 0.01 mg/L

The POR data then indicate an annual k 11 m/yr for

Brigh-ton, and k 3 m/yr for Estevan

The purpose here is to illustrate the fallacy of graphical data

representations and associated regressions between variables

that contain the same multiplier and the errors that pany an incorrect model choice This subject has been eluci-dated for natural treatment systems by Von Sperling (1999)

accom-As a hypothetical example, consider concentrations entering the wetland vary randomly between 0.2 and 1.2 g/m3 Like-wise, the concentrations leaving are also random between 0.1 and 0.3 g/m3 Therefore, the mean inlet concentration is 0.7 g/m3, the mean outlet concentration is 0.2 g/m3, and the resulting average concentration reduction is 71%

A set of 50 experiments is run, in which the hydraulic loading is varied linearly between 1 and 50 m/yr For any experiment, the inlet and outlet concentrations are indepen-dently random within the ranges selected (Figure 6.8) Not surprisingly, linear regression of the input/output concentra-tions explains virtually none of the variability There is a 72 o18% (mean o SD) concentration reduction, and that is all that may be determined

FIGURE 6.7 Outlet TP concentration versus inlet TP loading for Estevan, Saskatchewan, and Brighton, Ontario, treatment wetland

sys-tems The period of record past start-up was 4.25 years for Brighton, and nine years for Estevan (Unpublished data from city of Estevan and city of Brighton.)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Next, the correlation between pollutant load reduction

and inlet pollutant loading is examined Pollutant loading is

defined as hydraulic loading multiplied by concentration, for

both the inlet and outlet Pollutant load reduction is the

dif-ference between inlet and outlet pollutant loadings A

won-derful correlation is obtained with an R2 0.93, which makes

the data look great and makes us feel that we can use this

for design (Figure 6.9) Unfortunately, there is no connection

of performance to inlet loading, no matter how much this

load graph appeals to us The hydraulic loading appears in

both the ordinate and the abcissa, thus causing a stretching

of a random 2-D cloud along a diagonal axis The only useful

feature of the graph is the slope of the line, 0.70, which is the

correct result for the percent reduction Many examples of

this representation and analysis are to be found in the

treat-ment wetland literature (Knight et al., 1993; Hammer and

Knight, 1994; Vymazal, 2001), but they are of virtually no

value in design

The formerly popular first-order plug-flow model is then

examined The same hypothetical random data set is easily

manipulated to calculate a k-value for each pair of

input–out-put concentrations, or to provide a least-squares estimate that

best fits the entire data set, according to:

ln i o

(6.3)

The k-values so calculated average 32 m/yr The important

question is whether this model fits the data, so that it may

be used for predictions at specified hydraulic loading rates

The answer is that the first-order model fails and predicted

concentrations scatter randomly with respect to observed

concentrations

The subtle trap that has created trouble, in this example

and in some of the existing treatment wetland literature, is

the failure to check whether or not the model has any

valid-ity That can be done in a number of ways, but the easiest

method is the direct examination of the data trends expected

from the model For the simple first-order case, the fraction of

pollutant remaining is expected to decline exponentially with

detention time, or equivalently with the inverse of hydraulic loading, as indicated by Equation 6.3 In the present hypo-thetical example, log-linear regression of data in this manner

has an R2 0.000

6.3 MASS BALANCES

There are many measures and models for pollutant tions in treatment wetlands In this chapter, various defini-tions and options for system description are explored as a necessary precursor to the discussions of individual pollut-ants that follow in ensuing chapters

Individual concentration measurements are very often aged to eliminate some of the variability inherent in wet-lands The time average concentration, denoted by an overbar

C t

averaging period, dm

t 

Such average concentrations may be acquired from portional autosamplers, or computed from a time series

time-pro-An average mass flow of a chemical (QC) is the product

of the average flow and the flow-weighted (or mass average) concentration, defined by:

ˆ

t t

t t

t

1 0 1

1m

m

m m

This term is quite ambiguous, because it usually refers to the average of one or more synchronous samples for selected stream flows Such contemporaneous measures do not prop-erly reflect the internal chemical dynamics of the wetland, such as production of the chemical Further, dilution or

FIGURE 6.9 Load reduction versus incoming load for the

hypo-thetical, random data set of Figure 6.8

concentration due to rain (ET) or other unaccounted flows

renders this an imperfect measure of true removal

Neverthe-less, this terminology is frequently used in the literature

It is important to distinguish among the various measures of

global wetland chemical removal Some further definitions

used in this book are specified in the following text

Inlet Mass Loading Rates

 )) inlet mass loading, g/m ·d2

Acronyms are also often used for designating the

chemi-cal; for example, PLR denotes phosphorus loading rate A

chemical loading rate is a measure of the distributed

“rain-fall” equivalent of a chemical mass flow It does not imply the

physical distribution of water uniformly over the wetland

Mass Removal Rate

JA(Q Ci i Q Co o) (6.10)This represents the areal average amount of a chemical that gets

stored, destroyed, or transformed This single-number measure

of wetland performance can be misleading in the common

event of strong concentration gradients and removal gradients

Percent Mass Removal

This quantity links water losses and gains to chemical losses

m m

o i(6.11)

¤

¦¥

³µ´

¤

¦¥

³µ´

 eercent mass removal

%Qpercent flow reductioon

The term is less ambiguous than concentration reduction,

because it traces the chemical of interest, and accounts for

the effect of the quantity of water in which that chemical is

located However, the difficulties of contemporaneous surement remain

mea-The Utility of Reduction Numbers

It is very easy to compare the amounts of a pollutant in the inlet and outlet streams of a wetland, and to compute the per-centage difference Unfortunately, this information is of very limited use in design or in performance predictions, because

it reflects none of the features of the ecosystem, which are the target of design By implication, it would be necessary to rep-licate the wetland that produced the percentage data, as well

as to replicate the operating and environmental conditions that prevailed during data acquisition The second is clearly impossible, and past experience has given strong indications that the first is also difficult

The literature is replete with review papers that tabulate removals for a selected spectrum of wetlands (e.g., Strecker

et al., 1992; Cueto, 1993; Johnston, 1993).

The implication is that wetlands of a similar type will achieve a similar reduction Whereas such groups of data begin to elucidate the bounds of performance, the effects of size, loading, flow patterns, depth, and other design variables cannot be deduced from efficiency values alone

In some instances, the incoming concentration of a ticular chemical may be small for some period of time Then, due to measurement errors or small transfers from wetland, storages and productions may give outflow concentrations that are greater than the incoming values A one-time cal-culation of a “reduction efficiency” will properly reflect that condition as a (large) negative percent reduction At other times, a larger inflow concentration may be reduced by the wetland, leading to a positive percentage removal If the removal percentages are then averaged, the large negative value improperly dominates the calculation

par-As a result of these considerations, great care must be exercised in interpretation of percentage reduction values

Measurements of chemical composition of wetland inflows and outflows are the most obvious method of characterizing water quality functions However, such measurements by themselves can be very misleading A much better character-ization is achieved by computing the mass balance or budget for an individual chemical constituent

A proper mass balance must satisfy the following conditions:

1 The system for the mass balance must be defined

carefully A system in this context means a defined volume in space; this is often taken to be the sur-face water in the wetland in the case of a free water surface (FWS) wetland or the water in the media for a subsurface flow (SSF) wetland A pre-cise definition is needed to compute the change in

storage The mass balance is termed global when

the entire wetland water body is chosen as the

sys-tem In later chapters, it will be useful to compute

the internal mass balance, which is based on an

internal element or subdivision of the water body

2 The time period for totaling the inputs and outputs

must be specified It may be desirable to express

inflows and outflows in terms of rates, but these

must then be averaged over the time period chosen

3 All inputs and outputs to the chosen system must

be included The concept of mass conservation may

be invoked to calculate one or a group of material

flows A partial listing of some of the inflows and

outflows does not constitute a mass balance

4 Compounds undergo chemical reactions within a

wetland ecosystem Any production or

destruc-tion reacdestruc-tions that occur within the boundaries of

the chosen system are to be included in the mass

balance Reactions outside the boundary are not

counted, because an outflow must occur to

trans-port the chemical to the external reaction site, and

that is accounted as an outflow

5 Waterborne chemical flows are determined by

separate measurements of water flows and

con-centrations within those waters Therefore, an

accurate water mass balance is a prerequisite to

an accurate chemical mass balance

6 If at all possible, it is desirable to demonstrate

closure of the mass balance This is achieved by

independently measuring every component of

the mass balance The degree of closure is often

expressed as a percentage of total inflows

Unfor-tunately, closure has rarely been demonstrated for

any chemical in any wetland

The foundation for chemical mass balances is the wetland

water mass balance (see Chapter 2) Transfers of water to and

from the wetland follow the same pattern for both surface

and subsurface flow wetlands In treatment wetlands,

waste-water additions are normally the dominant flow; but under

some circumstances, other transfers of water are also

impor-tant The dynamic overall water budget for a wetland is:

“removal,” which may be positive or negative This lumping of all transfers to and from the water body is often unavoidable due to economic constraints It is possible to write a general mass balance equation for a generic chemical species:

omit-The time period for the global mass balance is of critical importance because of the time scale of interior phenomena Many wetlands, whether treatment or pristine natural, have long nominal detention times, which usually reflect long actual detention times A two-week detention is not uncommon If the wetland were in plug flow, an entering cohort of water would exit two weeks later Clearly, same-day samples taken from inlet and outlet should not be used to compute “removals.” In fact, wetland flow patterns are more complex than plug flow; the entering cohort breaks up, and pieces depart at various times after entry, some earlier and some later than the implied two-week detention This difficulty of synchronous sampling may be alleviated in the mass balancing process by selecting a mass balance period that spans several detention times.The removal term is the result of transfers to and from the soils and biomass compartments in the wetland, as well as of transfers to and from the atmosphere, and chemical conver-sions Those biomass and soils compartments dominate the overall wetland storage and transformations for most chemi-cals Therefore, the water body mass balance is very sensi-tive to small changes in transfers, reactions, and storages in biomass and soils The removal rate depends very strongly

on events in these solids compartments, and hence is mined in major part by the changing ecological state of the wetland Because wetland biological processes are more or less repetitive on an annual cycle, the long-term performance

deter-of the wetland is best characterized by global mass balances

that span an integer number of years Seasonal effects require

a time period of three months, which is usually long enough

to avoid storage errors and detention time offset

Removal in Equation 6.14 is an areal average However, in

most flow through wetlands, there is a strong gradient in the

unaveraged removal in the direction of flow As the downstream

wetland system “boundary” is moved successively further from

the inlet, the areal average removal rate decreases The average

removal rate depends on the size of the portion of the overall

wetland that is chosen for the global mass balance This

weak-ness of the global mass balance can be corrected by using the

internal mass balance that reflects distance effects

6.4 PROCESSES THAT CONTRIBUTE

TO POLLUTANT REMOVALS

A large number of wetland processes may contribute to the

removal or reduction of any given pollutant Here, some of the

most important are described and the commonly used rules

for quantification are presented More details are presented

in the following chapters for the most common chemicals of

interest The discussion here relates to localized phenomena

Removal processes must also be quantitatively placed in the

context of internal wetland hydraulics as well as the

topogra-phy and vegetative structure of the wetland

Many wetland reactions are microbially mediated, which

means that they are the result of the activity of bacteria or

other microorganisms Very few such organisms are found

free-floating; rather, the great majority are attached to solid

surfaces Often, the numbers are sufficient to form relatively

thick coatings on immersed surfaces

Transfer of a chemical from water to immersed solid

sur-faces is the first step in the overall microbial removal

mech-anism Those surfaces contain the biofilms responsible for

microbial processing, as well as the binding sites for sorption processes The following discussion analyzes the transport of dissolved constituents to reaction sites located in the biofilms that coat all wetland surfaces Mass transfer takes place both

in the biofilm and in the bulk water phase Roots are the locus for nutrient and chemical uptake by the macrophytes, and these are accessed by diffusion and transpiration flows The sediment–water interface is but one such active surface; the litter and stems within the water column comprise the domi-nant wetted area in FWS wetlands, and the media surface is the dominant area in SSF wetlands

Dissolved materials must move from the bulk of the water

to the vicinity of the solid surface, then diffuse through a stagnant water layer to the surface, and penetrate the biofilm while undergoing chemical transformation (Figure 6.10) This sequence of events has been described and modeled in the text

of Bailey and Ollis (1986), and is outlined here The case of zero wetland background concentration will be described here; but extension to the case of nonzero background is possible.The rate of transfer across the two films is:

J  ffer rate, g/m ·dreaction rate constant

2

b

FIGURE 6.10 Pathway for movement of a pollutant from the water across a diffusion layer and into a reactive biofilm The solid may be

sediment, a litter fragment, or a submerged portion of a live plant (From Kadlec and Knight (1996) Treatment Wetlands First Edition, CRC

Press, Boca Raton, Florida.)

 










Combining equations (the rate of transport of the pollutant

from the bulk water to the biofilm) is then:

D D

(6.18)

It is seen that this theory produces a local first-order rate of

overall reaction, which depends upon biofilm properties and

diffusion coefficients

In a field situation, it is also necessary to know the area

of biofilms that occupy a given area of wetland (Figure 6.11)

The overall removal rate from a wetland area Aw occurs from

a biofilm area of Ab, and hence the rate of removal is

wetland area, mbiofilm area,

2 2

b

A A

Data have been obtained for only a few FWS wetland

sys-tems, giving only a rough estimate of the magnitude of as If there is no vegetation, and only the wetland bottom serves as

the potential location of biofilms, the value of asa 1.00 If the emergent vegetation is considered an additional biofilm area,

a dense stand of plants can yield as ≈ 5 Inclusion of the litter

can further increase the value to as ≈ 10

This theory has been calibrated for treatment wetlands by

Polprasert and coworkers (Polprasert et al., 1998; Khatiwada and Polprasert, 1999a), who determined as in the range 2.2–2.9 Measurements of immersed vegetation surface area were made

at Arcata, California, and Houghton Lake, Michigan, and

pro-duced as in the range 1.0–9.0 (see Chapter 3)

Microbially mediated reactions are affected by ature Response is typically much greater to changes at the lower end of the temperature scale (15nC) than the warmer range (20–35nC) (Kadlec and Reddy, 2001) Processes regu-lating organic matter decomposition are affected by tempera-ture Similarly, all nitrogen cycling reactions (mineralization, nitrification, and denitrification) are affected by temperature The temperature coefficient (Q) varies from 1.05–1.37 for car-bon and nitrogen cycling processes under isolated conditions Phosphorus sorption reactions are least affected by tempera-ture with Q-values of 1.03–1.12 However, treatment wetlands

temper-Biofilm area = Ab

Wetland area = Aw

L W

Since biofilm growth is likely at the sediment-water interface as well as on

submerged litter and leaves, Ab > Aw.

FIGURE 6.11 Biofilms dominate the sediment–water interface, as well as the surfaces of the litter and standing dead material (Adapted

from Kadlec and Knight (1996) Treatment Wetlands First Edition, CRC Press, Boca Raton, Florida.)

display lesser temperature effects because of their complexity

(Kadlec and Reddy, 2001)

Several wetland chemical removal processes involve more

than one reaction and more than one chemical species Many

removal reactions create products that are themselves

con-taminants of interest An important example is the

(micro-bial) sequential conversion network for nitrogenous species:

organic N ammonia N oxidized N

gaseous N2

Each of the first three species is important in its own right as

a potential contaminant Both consumption and production

can occur; it is, therefore, misleading to isolate one species

and compute its “removal.”

Another example is the reductive dechlorination of a

chlori-nated organic compound Trichloroethylene has daughter

prod-ucts that are sequentially formed in a wetland environment:

trichloroethyleneldichloroethylenelvinyl chlooride

CO H O Cl2

(6.21)

In such cases, it is essential to utilize reaction models that

account for both production and destruction Each step may

individually have a simple model, such as first order; but in

combination, removal is quantitatively more complex

Various processes in wetland create product gases that are

released from the wetland environment to the atmosphere,

such as ammonia, hydrogen sulfide, dinitrogen, nitrous

oxide, and methane Wetlands also take in atmospheric

car-bon dioxide for photosynthesis and expel it from

respira-tory processes The mechanism of volatilization is further

discussed in Chapter 5 (for nitrous oxide, methane, and

car-bon dioxide), Chapter 9 (for ammonia), and Chapter 11 (for

hydrogen sulfide)

Chapter 7 deals with the removal of suspended solids Here,

it is noted that a first-order areal removal model is the

out-come of theory and practice Many pollutants partition to

sus-pended solids, and thus removal of those sorbed substances

also is expected to follow that model:

JkTSS•CTSS•K Cp• (6.22)where

suspended matter concentration, m

Partition coefficients relate the amount of sorbed pollutant

to the concentration in the water under equilibrium tions Three types of sorption isotherms are in common use

g

(6.23)

The sorption potential for the principal contaminants of interest is discussed in the chapters pertaining to those con-taminants Here, a few generalities are noted:

Sorption is important for phosphorus during the start-up period for a treatment wetland If initially absent in the sediments, phosphorus will be stored until the existing soils and sediments reach equi-librium with the overlying water If initially pres-ent, phosphorus may be released

Sorption is important for ammonia nitrogen in intermittently dosed or operated wetlands Short-term storage may be oxidized during drawdown periods

Sorption is important for hydrophilic organic chemicals, which partition strongly to the carbo-naceous content of wetland sediments

The water-phase concentration that is experienced

by wetland sediments and soils is pore water, which can have very different concentrations than the bulk water overlying those sediments and soils.Sorption sites are a partially renewable resource, because they may be added from the accumula-tion of newly formed sediments

Sorption may be partially irreversible, due to eralization of sorbed materials, or to the formation

min-of very strong chemical bonds

Linear sorption (Equation 6.23(a)) results in a theoretical first-order removal process at the local level

Sunlight can degrade or convert many waterborne substances Many microorganisms, including pathogenic bacteria and viruses, can be killed by ultraviolet radiation The effectiveness

is presumptively determined by the radiation dose rate as well

as the concentration of organisms Although this is cally a second-order process, the sunlight dose in the wetland

theoreti-is relatively constant in the long run, and the elimination rate

is therefore pseudo first order in the organism concentration

A wide variety of chemicals are also susceptible to removal,

in one or both of two ways Direct photolysis involves the

breakdown of the molecule, usually by the ultraviolet

compo-nent of the sunlight The nitrotoluenes are examples of readily

photolyzable substances Photooxidation occurs via reactions

with free radicals formed by the incident radiation, such as

alkylperoxy, hydroroxyl, and singlet oxygen radicals

(How-ard et al., 1991) Photodegradation has received essentially

no attention in treatment wetland research and development

Plants take up nutrients to sustain their metabolism They

may also take up trace chemicals found in the root zone,

which may then be stored, or in some cases, expelled as

gases Uptake is by the roots, which are most often located in

the wetland soils, although adventitious roots may sometimes

be found in the water column Submerged plants may absorb

nutrients and metals from the water column into stems and

leaves

If there is no infiltration, driven either by hydraulic head or

plant transpiration, to carry dissolved contaminants to

sorp-tion and reacsorp-tion sites and roots located below ground, then

diffusion is the dominant mechanism for vertical downward

movement of pollutants The presence of the soil matrix

pre-vents convection currents; therefore, the diffusive process is

further restricted to molecular diffusion The model for this

process is the diffusion equation:

The values of diffusion coefficients in pure water are of the

order of 2 – 10 r 10−5 m2/d at 25nC (i.e., 2.9 r 10−5 for COD,

and 7.6 r 10−5 for H2PO4) Values in the soil pore water are

likely to be lower, by about a factor of 4, because of tortuosity

and porosity effects

Some idea of the importance of the diffusive process may

be gained by examining the situation of mildly eutrophic

sur-face waters overlying a fully saturated peatland Reddy et al.

(1991) report soluble reactive phosphorus pore water

gradi-ents as large as 3.0 gP/m3·m in the top 20 cm of an Everglades

cattail-dominated peatland Under these circumstances, the

diffusion flux predicted by Equation 6.24 is:

Vertical flows of water in the upper soil horizon are also driven

by plant water uptake to support transpiration In aquatic and wetland systems with fully saturated soils or free surface water, the meteorological energy budget requires the vaporiza-tion of an amount of water sufficient to balance solar radiation and convective losses Some of this vaporization is from the water surface (evaporation); some is from the emergent plants (transpiration) Emergent plants “pump” water from the root zone to the leaves from which water evaporates through sto-mata, which constitutes the transpiration loss (see Figure 4.6)

In a densely vegetated wetland, transpiration dominates the combined process (evapotranspiration, which is abbreviated

as ET) (see Chapter 4) Water for transpiration must move through the soil to the roots That movement is vertically downward from overlying waters in FWS wetland situations, but directly from the flowing water in SSF wetlands

Thus, transpiration has the potential to move on the order

of 1 m/yr of water vertically downward to the root zone in

an FWS system That water carries with it the contaminant concentrations associated with the bottom layer of overlying water, which is the litter–benthic zone of the wetland This

flow is termed the transpiration stream (TS), and it draws

from pore water that is typically at a concentration ent from that of the bulk surface water In turn, the plant may block a portion of the dissolved pollutant, and take up

differ-a concentrdiffer-ation less thdiffer-an thdiffer-at of pore wdiffer-ater These fdiffer-actors combine to determine the amount of plant uptake (Trapp and Matthies, 1995; Gomez and Pardue, 2002):

JUTSrTSCFrCpw (6.25)

where

porewater concentration, g/mup

U

C J

 ttake flux, g/m ·dtranspiration stream,

transpira-Vertical Root Profiles

Plant roots are typically located in the top 30 cm of the soil, and most are in the top 20 cm (see Figure 2.29) However, rooting depths have been reported over a wide range For

example, for Phragmites, Moore et al (1994) reported 10 cm,

while Börner et al (1998) reported 150 cm U.S EPA (2000a)

recommends rooting media depths for FWS constructed

wetlands in the range 15–40 cm For other species, rooting

depth in FWS wetlands is typically 20–30 cm For instance,

Murkin et al (2000) report that roots were found entirely

within the top 20 cm for Phragmites, Typha spp., and

Scir-pus spp in a natural prairie marsh Similarly, Wentz (1976)

reported decreasing root biomass down to 45 cm for Carex

spp in the Houghton Lake wetland Given the vertical

pro-file of root density, there is presumptively a corresponding

vertical profile in the uptake of water and chemicals by the

plant However, such differential uptake is very difficult to

measure; consequently, plant uptake is usually assigned to

the vertically integrated root zone

Nutrient removal displays considerable seasonality for

ammonia at low loadings Accordingly, temperature is not

always an acceptable surrogate for seasonality for nitrogen

removal Vegetative uptake in temperate climates is

maxi-mum during spring, at moderate temperatures, but release

via decomposition is maximum during fall, also at moderate

temperatures Plants utilize phosphorus, nitrate, and

ammo-nium, and decomposition processes release nitrogen and

phosphorus back to the water On an instantaneous basis,

plant uptake can be important for many wetland systems

(Kadlec, 2005d)

One of the least studied aspects of pollutant transfer in

wet-lands is in the creation of new soils and sediments, with their

attendant chemical content Not all the dead plant

mate-rial undergoes decomposition Some small portions of both

aboveground and belowground necromass resist decay, and

form stable new accretions Such new stores of chemicals are

presumed to be resistant to decomposition The origins of

new sediments may be from remnant macrophyte stem and

leaf debris, remnants of dead roots and rhizomes, and from

undecomposable fractions of dead microflora and microfauna

(algae, fungi, invertebrates, bacteria)

The amount of such accretion has been quantified in only

a few instances for FWS wetlands (Reddy et al., 1991; Craft

and Richardson, 1993; Rybczyk et al., 2002), although

anec-dotal reports also exist (Kadlec, 1997a) Quantitative

stud-ies have relied upon either atmospheric deposition markers

(radioactive cesium or radioactive lead), or introduced

hori-zon markers, such as feldspar or plaster Either technique

requires several years of continued deposition for accuracy

6.5 CHARACTERIZATION OF INTERNAL

HYDRAULICS

The removal of pollutants within a constructed wetland

occurs through the diverse range of interactions between

the sediments, substrate, microorganisms, litter, plants, the

atmosphere, and the wastewater as it moves through the system The dynamics of water movement through the wet-land has a significant influence on the efficiency and extent

of these interactions Many of the important cal reactions rely on contact time between wastewater con-stituents and microorganisms and the associated substrate, whereas wastewater velocity can be an important deter-mining factor for other pollutant removal processes, such

biogeochemi-as mbiogeochemi-ass transfer Any short-circuiting or dead zones that occur within a wetland will, consequently, have an effect

on contact time as well as flow velocities and, therefore, impact on treatment efficiency Nonideal flow patterns can have very large effects upon the removal of pollutants in

wetland treatment systems (Kadlec et al., 1993; Carleton,

2002) It is, therefore, necessary to consider flow pattern effects and the related mixing in the design of wetland treatment systems

Three types of hydraulic inefficiencies may occur in treatment wetlands:

1 Internal islands and other topographical features

2 Preferential flow channels at a large distance scale

3 Mixing effects, such as water delays in litter layers and transverse mixing

The first mechanism is characterized by a gross areal

effi-ciency, which relates to the volumetric efficiency (eV) of the wetland, as discussed in Chapter 2 The second and third types are characterized by an equivalent set of well-mixed units in series, or other “mixing” model All three influence

a wetland’s ability to improve water quality

The main method by which wetland scientists and neers have gained information about internal hydraulic pro-cesses is through the use of inert tracers, which provide a means of tracking the movement of water through a wetland The theory and practice behind hydraulic investigations have predominantly evolved out of the field of chemical reaction engineering (Fogler, 1992; Levenspiel, 1995) The details of tracer testing are covered in Appendix B Here, a brief sum-mary is presented

A tracer test is conducted by introducing an impulse of an inert substance into the wetland inlet at time zero If water moved through the wetland in lock-step, such a tracer impulse would also exit as an impulse (a sharp spike of concentration) This result has never been observed in a wetland tracer test; the exit tracer is always a blurred, skewed bell-shaped curve

In the FWS wetland environment, there are mixing processes

on a number of different distance scales Expanses of open water permit development of surface wind-driven currents, which are matched by return flows in lower water layers Deeper parallel zones in the FWS wetland carry more flow because of the depth effect on hydraulic resistance These preferential channels may also be due to a lower vegetation density along some flow paths A tracer impulse added to

the incoming water provides a way to find such preferential

paths as the tracer will later be found preferentially in those

wetland zones Both natural and constructed FWS wetlands

display such flow variability (Figure 6.12) In particular, the

results for constructed wetlands indicate that it is not possible

to avoid such flow irregularities even with extreme care in

construction

There are also mixing effects in the vertical direction in

FWS wetlands Water may be moving more slowly near the

bottom because of the increased drag of the dense litter layer

Those slow-moving zones exchange chemical constituents

with adjacent faster-moving layers, and thus create vertical

mixing Dense plant clumps can effectively block flow even

though these are of very high void fraction Water in these

clumps can exchange constituents with the adjacent

micro-channels by diffusive processes All these effects combine to

form a complicated overall mixing pattern The result of such

mixing is evidenced in the blurring of a tracer impulse added

to the incoming water (Figure 6.12)

In a subsurface flow wetland, large-scale eddies and wind

mixing are absent However, preferential flow channels can

occur on a large scale Lateral inhomogeneities may

contrib-ute to nonuniform flow distribution across the width of the

wetland (Marsteiner, 1997) Evidence of this was found for a HSSF wetland at Benton, Kentucky, by internal sampling of tracer responses (Figure 6.14) An impulse of tracer (Rhoda-mine WT) was added to the inlet flow to this HSSF wetland Water was distributed across the entire width of the rectangular wetland The observed responses were considerably different at equidistant sampling points, indicating subsurface preferential paths Further, there is abundant evidence that vertical stratifica-tion occurs in gravel beds, with larger flows occurring at lower

elevations (Fisher, 1990; Marsteiner, 1997; Drizo et al., 2000)

The tracer concentrations that reach the HSSF wetland effluent are there blended to form an average outlet concentration The response of a typical HSSF wetland to an impulse tracer input is

a time-delayed bell-shaped curve (Figure 6.15)

The results of an impulse tracer test provide the

volumet-ric efficiency (eV) of the wetland, together with information

on the distribution of detention times in the system The first requirement of a valid tracer test is that the tracer be recovered nearly in its entirety at the wetland outlet To that end, a simple check is made by summing the tracer at the

24/25 hr

Dye Addition Line

10.9 m Outlet weir

Bromide Injection Line

21/261 hr

5 m

FIGURE 6.12 Tracer isopleths in a natural (a) and constructed (b) wetland In both cases, tracer was added uniformly across the inlet width

The theoretical location of the pulse centroid is shown by the horizontal line, labeled with elapsed time and theoretical detention time (a) Typha orientalis natural wetland in New Zealand (Data from A.B Cooper (1992) Coupling wetland treatment to land treatment: An innovative method for nitrogen stripping Proceedings of the 3rd International Conference on Wetland Systems for Water Pollution Control, Australian Water and Wastewater Association and IWA, Sydney, pp 37.1–37.9.) (b) Typha latifolia FWS constructed wetland in Ontario (Data from Herskowitz (1986) Listowel Artificial Marsh Project Report Ontario Ministry of the Environment, Water Resources Branch, Toronto, Ontario.) (From Kadlec and Knight (1996) Treatment Wetlands First Edition, CRC Press, Boca Raton, Florida.)

0 50 100 150 200 250 300 350

Time (min)

Path 1 Path 2 Path 3 Path 4 Path 5

1 2 3 4 5 Flow

FIGURE 6.14 Tracer concentrations at five stations normal for the flow direction in Gravel Bed Wetland #3 at Benton, Kentucky Although

these traces are not complete, it is clear that more tracer arrives sooner at Station 2 than at other stations (Data from TVA unpublished data.)

(From Kadlec and Knight (1996) Treatment Wetlands First Edition, CRC Press, Boca Raton, Florida.)

FIGURE 6.13 Results of a lithium tracer test of a 91-ha FWS wetland receiving 193,000 m3 /d Approximately 500 kg of lithium were

added The TIS model is calibrated by about 8 TIS (Data from Dierberg and DeBusk (2005) Wetlands 25(1): 8–25.)

0 50 100 150 200 250

FIGURE 6.15 Response of Cell 1 at Minoa, New York, to a tracer impulse The TIS model is calibrated to 14 TIS, and the volumetric

efficiency is 75% (Data from Marsteiner (1997) Subsurface Flow Constructed Wetland Hydraulics M.S Thesis, Clarkson University

(Potsdam, New York) 130 pp.)

0.00 0.02 0.04 0.06 0.08 0.10 0.12

 mmass of tracer in, g

mass of tracer out,

The detention time distribution (DTD) represents the time

various fractions of fluid (water in the case of the wetland)

spend in the reactor, and hence is the contact time distribution

for the system In a broader context, the DTD is the

probabil-ity densprobabil-ity function for residence times in the wetland This

time function is defined by

f t( )$  fraction of the incoming water whichh stays in thet

wetland forr a length of time between andt t $t

(6.27)where

(6.28)

The first numerator is the mass flow of tracer in the wetland

effluent at any time, t, after the time of the impulse addition

The first denominator is the sum of all the tracer collected

and thus should equal the total mass of tracer injected

The mean tracer detention time (T) is presumed to be the

actual mean detention time, and is calculated from

T 

c

¯

10

where

A wetland may have internal excluded zones that do not

inter-act with flow, such as the volume occupied by plant materials

In a steady-state system without excluded zones, the tracer

detention time (T) equals the nominal residence time (Tn)

This is true whether the flow patterns are ideal (plug flow

or well mixed) or nonideal (intermediate degree of mixing)

An adsorbing tracer will produce an artificially short

deten-tion time, which may then be erroneously presumed to result

from a large excluded zone An incorrect topography may

be due to either positive or negative differences between

T and Tn The ratio of tracer to nominal detention time is the volumetric efficiency:

V  wetland water volume, m3

There are a variety of reasons why the value of eV is ent from unity, as discussed previously in this chapter and in Chapter 2

differ-A second parameter which can be determined directly from the residence time distribution is the variance (S2), which characterizes the spread of the tracer response curve about the mean of the distribution, which is T:

or parallel flows of different velocities An adsorbing tracer will lead to a narrowed response pulse, and hence to an erro-neously low degree of mixing This measure of dispersive processes may be rendered dimensionless by dividing by the square of the tracer detention time:

TQ 2 2

The new parameter is SQ, the dimensionless variance of the

tracer pulse

Tracer testing is not an end in itself; rather, it is conducted to support the modeling and calculation of contaminant removals

in the wetland system Accordingly, the tracer information is combined with the local, or intrinsic, removal rate to produce the wetland outlet concentration There are many candidate models that may be used, which typically involve series and parallel combinations of two idealized flow elements: perfectly mixed units and plug flow sections (Figure 6.16) It is clear from numerous studies that treatment wetlands are neither plug flow nor well-mixed The tanks-in-series (TIS) model captures the important features of wetland DTDs that produce the skewed bell-shaped response The TIS model requires two parameters:

the number of “tanks” (N), and the mean tracer detention time

(T) As the model networks increase in complexity, such as the parallel path and finite stage models, they are able to resolve the

last bits of detail in the responses, but do so at the expense of

adding more calibration parameters In the extreme, it is

pos-sible to use complicated computer codes to model wetland tracer

responses (Martinez and Wise, 2003a; Keefe et al., 2004) In

this work, the TIS model is utilized as a spreadsheet

compro-mise between too many parameters and too little detail

Extreme Models

The two extremes of models are the single stirred tank and

plug flow Much of the literature about flow through lakes

assumes that the lake behaves as a single well-mixed unit (one

tank) In contrast, rivers are often conceptualized as plug flow

systems, possibly with some dispersion Much of the early

treatment wetland literature presumed plug flow, for

unspeci-fied reasons (U.S EPA, 1988b; Water Environment

Federa-tion, 1990) The wetland tracer studies of the early 1990s

made it apparent that neither extreme applied to FWS

wet-lands, and in many instances did not apply to HSSF systems

either Kadlec and Knight (1996) knew that plug flow did not apply, but reasoned that the plug flow assumption would be

“conservative,” provided that a background concentration was acknowledged It is now known that the plug flow assumption

is not always conservative (Kadlec, 1999a)

The danger in the plug flow model results from its sity to forecast extremely low effluent concentrations, when

propen-in reality, even mpropen-inor amounts of short-circuitpropen-ing preclude that from happening Therefore, the probability of design mistakes at long detention times is very high The temptation

to calculate plug flow rate constants is huge: just put numbers into Equation 6.33:

ln i o

FIGURE 6.16 A sample of various models to represent wetland tracer responses The plug flow model (A) produces an impulse output at one

detention time The well-mixed model (B) produces an exponential decline Models (C), (D), and (E) produce skewed bell-shaped responses.

such calculations: (1) Equation 6.33 does not apply to

synchro-nous samples, because of transport delay; and (2) there is no

indication of the amount of variability removed by this model

If no variability is removed, the model is a useless forecaster

The plug flow model is often an acceptable interpolator on

existing data sets (Kadlec, 1999a) Thus, if high flow and low flow

performance for a given system are known, a plug flow

interpo-lation is reasonable The difficulties arise when the model is used

for extrapolation to low outlet concentrations or for extrapolation

from one configuration to another In both cases, discrepancies

of a factor of two to five may easily be encountered (Figure 6.17)

The parameter P in Figure 6.17 is a modification of the number

of tanks in series, N, as discussed later in this chapter.

Despite these shortcomings, the wetland literature

con-tinues to espouse the plug flow formulation (e.g., Water

Envi-ronment Federation, 2001; Rousseau et al., 2004; Crites et al.,

2006) In this book, models that include the hydraulics and

configuration are used There is no loss of the ability to include

near-plug-flow in those situations where it is warranted

¤

¦¥

³µ´

When N 1, the gamma distribution becomes the

exponen-tial distribution Both the gamma distribution and the gamma

function are readily available in handbooks (e.g., Dwight,

1961), or as computer spreadsheet tools (e.g., IST and GAMMALN in Excel™) Equation 6.34 may easily

GAMMAD-be fit to tracer data by selecting N and T to minimize error

(e.g., SOLVER in Excel™) This is a gradient search

proce-dure, in which N and T are selected to minimize the sum of

the squared errors (SSQE) between the DTD model and the data Old textbook methods involve computation of the first and second moments of the experimental outlet concentra-tion distribution, which are related to tracer detention time and the number of TIS, respectively A serious failing of that moment method is that minor concentration anomalies on the

“tail” of the concentration response curve may yield spurious parameter values, and bad fits of the main part of the DTD The mode of the distribution (peak time), and its height, are

also useful in determining N and T, but the peak may not be

well defined For purposes of parameterization, it is noted that for the TIS model or gamma DTD distributions:

In the limit as N becomes very large, the gamma

distribu-tion becomes the plug flow (PF) distribudistribu-tion, with all water departing after exactly one detention time This limiting case does not exist for treatment wetlands Reported literature val-

ues are N  4.1 o 0.4 (mean o SE) for FWS wetlands, and N

 11.0 o 1.2 for HSSF wetlands (Tables 6.1–6.2) However,

1 10

FIGURE 6.17 Comparison of plug flow and P-k-C* areas required for specified percentage reductions Note that the areas are much larger

for low values of P, and for higher Damköhler numbers (Da  k/q) The fraction remaining to background is (C – C*)/(Ci – C*).

© 2009 by Taylor & Francis Group, LLC

nhrt (days)

tracer hrt (days)

Volumetric efficiency

Florida Everglades SAV Mesocosms 4 40 Lithium 75 3.6 4.0 111 4.0 1

Florida Everglades SAV Mesocosms 4 80 Lithium 90 7.2 7.7 107 7.7 1

Florida Everglades SAV Mesocosms 4 120 Lithium 96 10.8 9.0 83 9.0 1

Florida Everglades Algae Mesocosms 6 44 Lithium 86 11.1 13.1 118 1.4 1

Florida Everglades Algae Mesocosms 18 34 Lithium 75 6.5 16.6 256 1.4 1

Australia Richmond Open Water Open Water 400 0.5 RWT — 5.70 4.63 81 1.6 2

Australia Richmond SAV SAV 400 0.5 RWT — 6.30 5.00 79 5.5 2

Florida Champion Mixed Emergent E 1,000 34 Lithium 82 0.97 0.88 91 10.7 3

Florida Champion Mixed Emergent F 1,000 68 Lithium 105 3.38 2.50 74 2.0 3

Florida Everglades SAV Test Cells 2,000 71 RWT 83 5.6 5.9 105 5.9 1

Florida Everglades Algae Test Cells 2,000 48 Lithium 82 10.6 11.6 109 3.1 1

Florida Champion Mixed Emergent C 2,000 34 Lithium 90 2.59 1.12 43 4.0 3

Florida Champion Mixed Emergent D 2,000 57 Lithium 58 11.83 9.66 82 3.5 3

Florida Everglades Cattails Test Cells 2,457 36 Lithium 95 3.6 2.1 60 4.3 1

California Sacramento Bulrushes 7B 2,926 55 Lithium 76 4.8 4.7 98 4.2 4

California Sacramento Bulrushes 9B 2,926 56 Lithium 78 4.8 6.4 133 5.2 4

Florida Champion Mixed Emergent A 4,000 34 Lithium 64 7.48 4.68 63 6.3 3

Florida Champion Mixed Emergent B 4,000 48 Lithium 37 21.45 17.40 81 3.6 3

Arizona Tres Rios Bulrushes H2 9,100 49 Bromide 95 4.7 2.8 60 5.8 5

Arizona Tres Rios Bulrushes H1 9,200 49 Bromide 80 4.3 3.3 77 8.6 5

Arizona Tres Rios Bulrushes C2 12,800 52 Bromide 99 3.0 1.8 62 7.2 5

Arizona Tres Rios Bulrushes C1 13,400 67 Bromide 79 3.0 2.4 79 6.1 5

Illinois Des Plaines Cattails EW3 20,000 60 Lithium 98 12.3 8.4 68 2.7 6

Florida Iron Bridge Mixed Emergent 3 56,680 — Bromide 91 2.57 1.34 52 1.4 7

Florida Iron Bridge Mixed Emergent 4 56,680 — Bromide 95 8.97 2.28 25 2.1 7

Florida Iron Bridge Mixed Emergent 7 117,409 — Bromide 97 13 2.63 20 3.1 7

Florida Iron Bridge Mixed Emergent 8 121,457 — Bromide 112 2.95 1.24 42 0.3 7

Florida Iron Bridge Mixed Emergent 1 230,769 — Bromide 109 4.53 1.38 30 1.3 7

Florida Everglades Cattails Test Cells 2,457 36 Lithium 95 3 .6 2.1 60 4.3 1

California Sacramento Bulrushes 7B 2,9 26 55 Lithium 76 4.8...

California Sacramento Bulrushes 9B 2,9 26 56 Lithium 78 4.8 6. 4 133 5.2 4

Florida Champion Mixed Emergent A 4,000 34 Lithium 64 7.48 4 .68 63 6. 3 3

Florida